integral imaging can be understood as the number of different pixel datawithin a certain viewing angle. The angular resolution is determined by thenumber of pixels on the flat-panel display for a single elemental image, andthus it is limited by the finite pitch of pixels on the flat-panel display. Whenthe other viewing characteristics are fixed, either more pixels or a higher-resolution flat-panel display are needed for the higher angular resolution.

3.3 Implementation of a Lenticular 3D Display

Figure 3.10 shows the general process for implementing a lenticular multi-view display. In practice, the lenticular multi-view display is implemented bycombining the array of cylindrical lenses and flat-panel displays, such asLCDs and OLEDs. The specifications of the cylindrical lens and flat-paneldisplay determine the viewing parameters of a lenticular multi-view-displaysystem. Therefore, it is important to analyze the relation between thespecification of the lenticular lens and display device and the viewingparameters for manufacturing the lenticular multi-view display. The latter canbe derived from the relation between the viewing parameters of the multi-viewdisplay and the optical properties of the lenticular lens, as explained inSection 3.1. Unfortunately, the molding process for a lenticular sheet has ahigh cost. Lenticular lenses with a similar specification calculated bytheoretical equations are used in the following examples. In general, themajor specification of the lenticular lens is defined by lens per inch (LPI), i.e.,how many lenticules are arranged in one inch and represent the pitch of thelenticule. The lenticular lens is manufactured to have a focal length thatcorresponds to its thickness. Figure 3.11 shows the commercialized lenticularlenses that have a LPI of 25, 40, and 75. There are also various kinds of

Figure 3.10 Process of the fabrication of lenticular multi-view display.

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lenticular lenses commercially available, the detailed specifications of whichare provided in Table 3.1.15

The optimum viewing distance of a multi-view system is calculated by

D ¼ fNpp

Npp � pl, (3.19)

where N is the number of views, pp is the pixel pitch of the display, pl is thepitch of the lenticule, f is the focal length of the lenticular sheets, and D is theoptimum viewing distance.

In order to implement a prototype of a multi-view display using alenticular sheet, a LCD display that has a size of 24 in., a resolution of3840� 2400, and a pixel size of 124.5 mm is used. The desired viewing

Figure 3.11 Captured images of commercially available lenticular sheets (20, 40, and75 LPI).

Table 3.1 Specifications of commercially available lenticular sheets from one particularmanufacturer.15

LPI Thickness (in.) Lenticule Width (in.) Viewing Angle (deg.)

40 0.0330 0.0251 4950 0.0240 0.0200 5462 0.0270 0.0161 4275 0.0180 0.0133 49100 0.0215 0.0101 31100 0.0140 0.0100 47150 0.0103 0.0067 43

57Design and Implementation of Autostereoscopic Displays

parameters of the prototype are the seven views with an interval of viewscorresponding to a binocular distance of 65 mm. The lenticular sheet with a3.2-mm focal length and a LPI of 25 is chosen to get the desiredspecifications. The parameters of the prototype are calculated by the aboveequations, and the prototype has an optimum viewing distance of 1433 mm,an effective pixel pitch of 145.5 mm, and a gap between the display andlenticular sheet of 3.2 mm.

As shown in Fig. 3.12(a), the lenticular-lens multi-view display has amoiré pattern problem that also appears in the parallax-barrier multi-viewdisplay. The moiré pattern in the multi-view display is due to theinterference created by the stacked pair of 1D periodic structures: alenticular lens (or parallax barrier) and a sub-pixel structure of LCD. Themoiré pattern can be eliminated simply by placing the lenticular lensperpendicular to the sub-pixel structure of a LCD and lenticular sheet, asshown in Fig 3.12(b). The moiré pattern problem will be solved by theslanted lenticular method (see Chapter 4).

The next step involves arranging the lenticular sheet on a LCD. Acalibration pattern is used for this process. In the example system, thecalibration pattern is composed of four black and one white view images.The white view image is usually located at the center as shown in Fig. 3.13.Figures 3.14(a) and (b) show the captured images of the prototype aftercalibration at the optimum viewing distance of 1433 mm and out of theoptimum viewing distance, respectively. At the optimum viewing distance,the calibration pattern is observed in the entire effective display area. On theother hand, the calibration pattern forms a white stripe when the prototype isobserved out of the optimum viewing distance. Away from the viewingdistance, the observed pixel area in the base image is increased compared to

Figure 3.12 Moiré problem in the lenticular type multi-view display: (a) with moiré(b) without moiré.

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the optimal condition, resulting in a different sampling period.16 Thisphenomenon occurs because the sampling distance of the view imagedepends on the viewing distance, as explained in Section 3.1.

Figure 3.15 shows the implemented lenticular multi-view-display proto-type. After rotating the LCD display to solve the moiré pattern problem, thelenticular sheet is attached to the display surface with a calibration process,whereby the optimal lens position and viewing distance are found. In order toinspect the generation of each view image from the prototype, the base imagerepresenting the seven different views is calculated by the mapping methoddescribed in Section 3.3. The base image used in the experiment appears inFig. 3.16, and each view image captured in a different viewing positionappears in Fig. 3.17.

Figure 3.13 View images and the interwoven calibration image.

Figure 3.14 Captured images of calibration patterns (a) at one viewpoint and (b) out of theviewpoint.

59Design and Implementation of Autostereoscopic Displays

3.4 Implementation of a Parallax-Barrier Display

The parallax-barrier multi-view display is a representative multi-view-displaymethod;1,2 its simple configuration provides flexibility to the choice ofspecifications. Parallax barriers can be made of passive devices, such as

Figure 3.15 Captured image of implemented lenticular multi-view-display prototype.

Figure 3.16 Base image for the implemented lenticular multi-view-display prototype.

60 Chapter 3